LALComputeAM.h

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/*
*  Copyright (C) 2007 John Whelan, Reinhard Prix
*  Copyright (C) 2007 Jolien Creighton, Maria Alessandra Papa, Steve Berukoff
*
*  This program is free software; you can redistribute it and/or modify
*  it under the terms of the GNU General Public License as published by
*  the Free Software Foundation; either version 2 of the License, or
*  (at your option) any later version.
*
*  This program is distributed in the hope that it will be useful,
*  but WITHOUT ANY WARRANTY; without even the implied warranty of
*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
*  GNU General Public License for more details.
*
*  You should have received a copy of the GNU General Public License
*  along with with program; see the file COPYING. If not, write to the
*  Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
*  MA  02110-1301  USA
*/
#ifndef _LALCOMPUTEAM_H
#define _LALCOMPUTEAM_H
 
#ifdef __cplusplus
extern "C" {
#endif
 
/**
 * \defgroup LALComputeAM_h Header LALComputeAM.h
 * \ingroup lalpulsar_coh
 * \author S.J. Berukoff, Reinhard Prix, John Whelan
 * \date 2007
 *
 * \brief Header-file for computing antenna-pattern components for amplitude demodulation.
 *
 * <tt>\#include <lal/LALComputeAM.h></tt>
 *
 * In order to compute the optimal statistic for pulsar searches, one must take account of the
 * various modulations that change the emitted, (fairly) simple sinusoid into a non-trivial function
 * of parameters.  The frequency evolution of the signal (spindown effects, Doppler modulation, etc.)
 * have already been accounted for; this routine filters the amplitude modulation effects.
 */
/** @{ */
 
/*---------- exported INCLUDES ----------*/
#include <math.h>
#include <lal/DetResponse.h>
#include <lal/DetectorSite.h>
#include <lal/LALBarycenter.h>
#include <lal/DetectorStates.h>
#include <lal/PSDutils.h>
 
/* ---------- exported data types -------------------- */
 
/**
 * This structure contains the per-SFT (weighted) antenna-pattern functions
 * \f$ \widehat{a}_{X\alpha}, \widehat{b}_{X\alpha} \f$ ,
 * with \f$ \alpha \f$ the SFT-index, and \f$ X \f$ the IFO index. The per-IFO summed antenna-pattern coefficients
 * for detector X are
 * \f$ \widehat{A}_X,\widehat{B}_X,\widehat{C}_X \f$ and their determinant \f$ \widehat{D}_X=\widehat{A}_X \widehat{B}_X - \widehat{C}_X^2 \f$ .
 *
 * \p See Sec.4.1 in CFSv2 notes (https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=T0900149&version=4)
 */
typedef struct tagAMCoeffs {
  REAL4Vector     *a;          /**< (weighted) per-SFT \f$ X\alpha \f$ antenna-pattern function \f$ \widehat{a}_{X\alpha} \f$ */
  REAL4Vector     *b;          /**< (weighted) per-SFT \f$ X\alpha \f$ antenna-pattern function \f$ \widehat{b}_{X\alpha} \f$ */
  REAL4           A;           /**< summed antenna-pattern matrix coefficient: \f$ \widehat{A}_X = \sum_{\alpha} \widehat{a}^2_{X\alpha} \f$ */
  REAL4           B;           /**< summed antenna-pattern matrix coefficient: \f$ \widehat{B}_X = \sum_{\alpha} \widehat{b}^2_{X\alpha} \f$ */
  REAL4           C;           /**< summed antenna-pattern matrix coefficient: \f$ \widehat{C}_X = \sum_{\alpha} \widehat{a}_{X\alpha}\,\widehat{b}_{X\alpha} \f$ */
  REAL4           D;           /**< determinant \f$ \widehat{D}_X = \widehat{A}_X \widehat{B}_X - \widehat{C}_X^2 \f$ */
} AMCoeffs;
 
/**
 * This structure contains the parameters for the routine.  They include:
 */
typedef struct tagAMCoeffsParams {
  BarycenterInput      *baryinput;  /**< data from Barycentring routine */
  EarthState           *earth;      /**< from XLALBarycenter()           */
  EphemerisData        *edat;       /**< the ephemerides                */
  LALDetAndSource      *das;        /**< det and source information     */
  LALFrDetector        *det;        /**< detector geometry              */
  REAL4                polAngle;    /**< polarization angle             */
} AMCoeffsParams;
 
/**
 * Struct holding the "antenna-pattern" matrix \f$ \mathcal{M}_{\mu\nu} \equiv \left( \mathbf{h}_\mu|\mathbf{h}_\nu\right) \f$ ,
 * in terms of the multi-detector scalar product.
 
  \f[
  \newcommand{\Ad}{\widehat{A}}
  \newcommand{\Bd}{\widehat{B}}
  \newcommand{\Cd}{\widehat{C}}
  \newcommand{\Ed}{\widehat{E}}
  \newcommand{\Dd}{\widehat{D}}
  \newcommand{\ah}{\hat{a}}
  \newcommand{\bh}{\hat{b}}
  \newcommand{\M}{\mathcal{M}}
  \newcommand{\S}{\mathcal{S}}
  \newcommand{\Tsft}{T_{\mathrm{sft}}}
  \newcommand{\Nsft}{N_{\mathrm{sft}}}
  \f]
 
This matrix can be shown to be generally expressible as
 * \f{equation}{
 * \M_{\mu\nu} = \S^{-1}\,\Tsft\,\begin{pmatrix}
 *  \Ad & \Cd &   0 & -\Ed \\
 *  \Cd & \Bd & \Ed &    0 \\
 *    0 & \Ed & \Ad &  \Cd \\
 * -\Ed &   0 & \Cd &  \Bd \\
 * \end{pmatrix}
 * \f}
 * where \f$ \S^{-1} \equiv \frac{1}{\Nsft}\sum_{X\alpha} S^{-1}_{X\alpha} \f$ characterizes the overall multi-detector noise-floor.
 * The sum is over all detectors \f$ X \f$ and all SFTs \f$ \alpha \f$ from each detector. The nonzero matrix coefficients are expressible as
 * \f{align}{
 * \Ad &\equiv \sum_{X\alpha} \left|\ah_{X\alpha}\right|^2 \,,\\
 * \Bd &\equiv \sum_{X\alpha} \left|\bh_{X\alpha}\right|^2 \,,\\
 * \Cd &\equiv \mathrm{Re} \sum_{X\alpha} \ah_{X\alpha}^{\,*} \,\bh_{X\alpha} \,,\\
 * \Ed &\equiv \mathrm{Im} \sum_{X\alpha} \ah_{X\alpha}^{\,*} \,\bh_{X\alpha} \,,\\
 * \f}
 * in terms of the noise-weighted atenna-functions are \f$ \ah_{X\alpha} \equiv \sqrt{w_{X\alpha}}\,a_{X\alpha} \f$ ,
 * and \f$ \bh_{X\alpha} = \sqrt{w_{X\alpha}}\,b_{X\alpha} \f$ , with per-SFT noise-weights
 * \f$ w_{X\alpha} \equiv \frac{S^{-1}_{X\alpha}}{\S^{-1}} \f$ .
 *
 * \note One reason for storing the un-normalized \f$ \{\Ad,\,\Bd,\,\Cd,\,\Ed\} \f$ and the normalization-factor \f$ \S^{-1}\,\Tsft \f$ separately
 * is that the former are of order one, while the latter is generally very large, and so it has numerical advantages for parameter-estimation
 * to use that fact.
 */
typedef struct tagAntennaPatternMatrix {
  REAL4 Ad;             //!< \f$ \Ad \f$
  REAL4 Bd;             //!< \f$ \Bd \f$
  REAL4 Cd;             //!< \f$ \Cd \f$
  REAL4 Ed;             //!< \f$ \Ed \f$
  REAL4 Dd;             //!<  determinant factor \f$ \Dd \equiv \Ad \Bd - \Cd^2 - \Ed^2 \f$ , such that \f$ \det\M = \Dd^2 \f$
  REAL8 Sinv_Tsft;      //!< normalization-factor \f$ \S^{-1}\,\Tsft \f$ (using single-sided PSD!)
} AntennaPatternMatrix;
 
/** Multi-IFO container for antenna-pattern coefficients \f$ a_{X\alpha}, b_{X\alpha} \f$ and atenna-pattern matrix \f$ \mathcal{M}_{\mu\nu} \f$ */
typedef struct tagMultiAMCoeffs {
  UINT4 length;                 /**< number of IFOs */
  AMCoeffs **data;              /**< noise-weighted AM-coeffs \f$ \widehat{a}_{X\alpha} \f$ , and \f$ \widehat{b}_{X\alpha} \f$ */
  AntennaPatternMatrix Mmunu;   /**< antenna-pattern matrix \f$ \mathcal{M}_{\mu\nu} \f$ */
} MultiAMCoeffs;
 
 
/*---------- exported Global variables ----------*/
 
/*---------- exported prototypes [API] ----------*/
 
int XLALComputeAntennaPatternCoeffs( REAL8 *ai, REAL8 *bi, const SkyPosition *skypos, const LIGOTimeGPS *tGPS, const LALDetector *site, const EphemerisData *edat );
 
int XLALWeightMultiAMCoeffs( MultiAMCoeffs *multiAMcoef, const MultiNoiseWeights *multiWeights );
 
AMCoeffs *XLALComputeAMCoeffs( const DetectorStateSeries *DetectorStates, SkyPosition skypos );
MultiAMCoeffs *XLALComputeMultiAMCoeffs( const MultiDetectorStateSeries *multiDetStates, const MultiNoiseWeights *multiWeights, SkyPosition skypos );
 
AMCoeffs *XLALCreateAMCoeffs( UINT4 numSteps );
void XLALDestroyMultiAMCoeffs( MultiAMCoeffs *multiAMcoef );
void XLALDestroyAMCoeffs( AMCoeffs *amcoef );
REAL4 XLALComputeAntennaPatternSqrtDeterminant( REAL4 A, REAL4 B, REAL4 C, REAL4 E );
void XLALSetAntennaPatternMaxCond( REAL4 max_cond );
void XLALSetAntennaPatternIllCondDeterminant( REAL4 illCondDeterminant );
 
/** @} */
 
#ifdef __cplusplus
}
#endif
 
#endif /* _LALCOMPUTEAM_H */